A Faster-Than Relation for Semi-Markov Decision Processes

TL;DR

This paper introduces a faster-than relation for semi-Markov decision processes to compare system timing, examines its properties, and identifies conditions to prevent anomalies in concurrent system modeling.

Contribution

It defines and analyzes a new faster-than relation for semi-Markov decision processes, exploring its compositional properties and conditions to avoid parallel timing anomalies.

Findings

The faster-than relation is not a precongruence under parallel composition.

Decidable conditions are identified to prevent parallel timing anomalies.

The study advances understanding of timing relations in concurrent systems.

Abstract

When modeling concurrent or cyber-physical systems, non-functional requirements such as time are important to consider. In order to improve the timing aspects of a model, it is necessary to have some notion of what it means for a process to be faster than another, which can guide the stepwise refinement of the model. To this end we study a faster-than relation for semi-Markov decision processes and compare it to standard notions for relating systems. We consider the compositional aspects of this relation, and show that the faster-than relation is not a precongruence with respect to parallel composition, hence giving rise to so-called parallel timing anomalies. We take the first steps toward understanding this problem by identifying decidable conditions sufficient to avoid parallel timing anomalies in the absence of non-determinism.